School of Computer Science THE UNIVERSITY OF BIRMINGHAM Ghost Machine


Notes for presentation on Monday 24th July scheduled as

Gaps Between Human and (Current) Artificial Mathematics
Conference submission (with references added):

11:40 AM

I'll try to present a new slant:

Universe-level Epigenetics

(DRAFT: Liable to change)
Conference details: ICCM Warwick University July 2017
Aaron Sloman
School of Computer Science, University of Birmingham

This is part of the Meta-Morphogenesis (M-M) project

Including the theory of evolved construction kits

This paper is
Abbreviated link
A PDF version may be added later.

A partial index of discussion notes is in

Abstract published for ICCM
The Turing-inspired Meta-morphogenesis project begun in 2011 was partly motivated by deep gaps in our understanding of mathematical cognition and other aspects of human and non-human intelligence and our inability to model them. The project attempts to identify previously unnoticed evolutionary transitions in biological information processing related to gaps in our current understanding of cognition. Analysis of such transitions may also shed light on gaps in current AI. This is very different from attempts to study human mathematical cognition directly, e.g. via observation, experiment, neural imaging, etc. Fashionable ideas about "embodied cognition", "enactivism", and "situated cognition", focus on shallow products of evolution, ignoring pressures to evolve increasingly disembodied forms of cognition to meet increasingly complex and varied challenges produced by articulated physical forms, multiple sensory capabilities, geographical and temporal spread of important information and other resources, and "other-related meta-cognition" concerning mental states, processes and capabilities of other individuals. Computers are normally thought of as good at mathematics: they perform logical, arithmetical and statistical calculations and manipulate formulas, at enormous speeds, but still lack abilities in humans and other animals to perceive and understand geometrical and topological possibilities and constraints that (a) are required for perception and use of affordances, and (b) play roles in mathematical, and proto-mathematical, discoveries made by ancient mathematicians, human toddlers and other intelligent animals. Neurally inspired, statistics-based (e.g."deep learning") models cannot explain recognition and understanding of mathematical necessity or impossibility. A partial (neo-Kantian) analysis of types of evolved biological information processing capability still missing from our models may inspire new kinds of research helping to fill the gaps. Had Turing lived long enough to develop his ideas on morphogenesis, he might have done this.

Keywords (expanded):
Archimedes; Euclid; Kant; geometry; topology; cognition; evolution; development; abstraction; non-empirical; non-contingent; toddler-theorems; disembodiment;

Understanding natural intelligence

Including squirrel intelligence, crow intelligence, elephant intelligence, toddler intelligence, octopus intelligence, intelligence of ancient mathematicians like Archimedes, ...

Current AI models/explanations don't even come close.
Neither (as far as I know) do psychology, neuroscience, philosophy, ...
A few examples:

Several kinds of gap in our knowledge, e.g.

(a) Forms of intelligence used by humans (young and old) and other animals
      (including individual variations within species, and during development)
(b) What mechanisms make those forms of intelligence possible
      (including forms of representation and manipulation of information)
(c) How those forms of evolution evolved, and
(d) How they develop in individuals
(e.g. linguistic competences and topological and geometrical reasoning competences in humans).

The M-M hypothesis

Perhaps understanding more about intermediate stages in evolution of various kinds of natural intelligence will draw attention to gaps in our ideas about modelling and replication of natural competences.

Including intelligence of various known and conjectured intermediate life forms in the more or less distant past -- sometimes inferred indirectly from likely challenges faced by evolutionary ancestors.

Thinking in detail about new challenges and opportunities produced by early evolutionary developments may provide new ideas about evolved solutions.

What Can We Learn From Conjectured Evolutionary Transitions?

An example of crow intelligence (Betty reported in 2002):
For more information about Betty see Oxford Ecology Laboratory
Online videos show that in order to get a bucket of food out
of a vertical tube, she made hooks out of straight pieces of
wire found nearby, in at least four different ways.

  • What new forms of intelligence were required by the transition from water-based to land-based-life, or from one kind of terrain to another, or when a new type of predator or prey turned up, or when articulated body parts became independently controllable, or when remote-sensing mechanisms evolved, or when various kinds of flight developed, or when offspring were born or hatched unable to feed, or to move, themselves, or when mating required cooperation?

  • possibility impossibility necessity

Problem: educational gaps in our culture

Part of the problem is that some of the hardest questions are not widely understood by researchers, because formulating the questions accurately requires concepts from epistemology, and metaphysics which hardly anyone learns at school, nowadays.

E.g. the distinction between empirical and non-empirical knowledge, and the closely related, but different, distinction between contingent and non-contingent (necessary) truths and falsehoods, both discussed by Immanuel Kant in 1781.

Necessity, impossibility, and related concepts have nothing to do with statistical evidence or probabilities.

Those concepts are often assumed to be based on "possible-world semantics" (e.g. what is true in this world and in all possible alternative worlds).

But for a child or non-human animal, or someone making a topological discovery, impossibility has nothing to do with alternative complete worlds.

Only possible alternatives to a localised portion of this world are relevant.
A more detailed, but still incomplete, analysis was presented in my 1962 DPhil Thesis, defending Kant.

"If a problem is too hard to solve,
try to find a related harder one"

(I can't now recall where I learnt that.)


Where do various forms of intelligence fit in the scheme of things?



If we look beyond our planet we find far more structures of various kinds on various scales: with new discoveries being added constantly.

Those are structures found by physicists/cosmologists

E.g. see Max Tegmark's book:
Our mathematical universe, my quest for the ultimate nature of reality

What features make physical stuff able to implement and bring into existence implementations of minds and their properties?

However all the above summarised structures on our planet must somehow have been produced by the structures studied by physicists.

So any adequate fundamental physical theory needs to be capable of playing a deep role in explanations of the origins and workings of all the structures on our planet (and perhaps other more complex structures in other parts of the universe, unknown to us).

But one of the things we have learnt from developments in computer science and engineering in the last 70 years or so is that there are different sorts of deep roles that a single powerful explanatory mechanism can have.

For example there is now a huge variety of uses of computers, differing enormously in physical scale, in type of function, in kinds of applications, in functions served: and all of these depend on a common substratum that can take different but mathematically equivalent forms, including large arrays of bistable switches that can be made to change their on/off patterns under the control of other switches.





Figure adapted from: Jackie Chappell and Aaron Sloman, 2007,
"Natural and artificial meta-configured altricial information-processing systems," International Journal of Unconventional Computing, 3, 3, pp. 211--239, ==========================================================================

Can we extend some those ideas about epigenesis in organisms to epigenesis in the universe as a whole?

For now let's consider this only in relation to evolution on one planet, using ideas developed in the Meta-Morphogenesis project
especially the work on fundamental and derived construction kits used by natural selection.
(still extending ideas published in sloman2013 sloman2017


A sketch of epigenesis on a universal scale (a)


A sketch of epigenesis on a universal scale (b)



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Last updated: 10 Jul 2017; 16 Jul 2017

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School of Computer Science
The University of Birmingham